omenti

measurement grounded activity recommendations

A minipost on staying healthy

 

For the last twenty years or so it's been increasingly clear that exercise is a powerful drug large benefits and few if any downsides.  Recommendations for how much across wide ranges of populations are improving, but historically have been educated guesses and extrapolations based on inadequately sized studies.  Fitbits, Apple watches and other wearables that measure and record movement are revolutionizing how the science is done.  Study sizes and data quality have increased dramatically and are being correlated with real measures of health from physicals and other widespread measures.  New targeted recommendations based on the improved studies are emerging with recommendations for various age groups and differing physical abilities and medical conditions, acceptable sedentary behavior, a better understanding of the depression-fighting power of physical movement and so on.  

 

The British Journal of Sports Medicine has dedicated their latest issue to the new device-grounded WHO physical activity recommendations and has posted it outside their paywall. Perhaps most important is the WHO 2020 Guidelines article, but most of the articles are interesting and written for the non-specialist.  They also posted an informative twenty minute podcast episode:

BMJ talk medicine · The 2020 WHO Guidelines on Physical Activity with Prof Fiona Bull and Dr Juana Willumsen. Ep #456

 

If you're looking for some serious strength and conditioning exercises, Sarah has put together a few on her YouTube page. They're aimed more at those already in good shape who don't have access to a gym.  Just look for those labeled strengthening and conditioning - the rest are aimed at beginning volleyball players.  At the other end of the scale walking is an excellent exercise.

And a simple recommendation from me.  Getting out in the cold weather away from people is an excellent way to get exercise.  As a native Montanan I offer one bit of advice on dressing for the cold: layered clothing.  It can make the difference between a pleasant bit of outdoor activity and being cold, wet and miserable. 

 

 

 

chindōgu

a minipost

Several people have written asking for educational projects to occupy their kids during the pandemic.  I've answered with a number of ideas, but it hit me chindōgu could be the perfect ticket for many.  It's the absurd Japanese art of useless inventions aimed at solving everyday problems with roots in Rube Goldberg machines and the art of the kludge - a clever but inelegant solution to a problem.   A number of good examples are shown here.  I've recommended this approach to a number of middle and high school teachers.  At least one has had a lot of fun with it making a "how to program things" module more fun.  It's also become a recreational art form at an animation studio you've heard about.

 

Thinking that way can be unexpected powerful.  It cuts through barriers combining critical thinking and play with the goal of humor.  Failure is fine and can be a powerful learning experience. Simone Giertz has been credited with getting more teenage girls interested in engineering than other person or program.  She's famous for useless robots - "shitty robots" as she calls them.   Here's her TED talk (one of the few useful TED talks I've seen).  

 Here's her YouTube channel.  Earlier pieces may be more accessible to beginners as she's become more sophisticated in her craziness.  And she has done much of this with brain cancer.  A remarkable inspiration. 

 

So start off small with supplies around the house and just have fun.  There aren't any downsides and you can spend as much or as little as you want.  You're only limited by your imagination and sense of humor.  And if you are building them, you can draw or write about them.   

 

 

good tide-ings

Jheri asked a good question about the tides.  First you need to watch Henry Reich's piece on the subject.  (His goal is to move quickly so you might have to stop every now and again and rewatch a segment.)

Basically differential gravity - the water on the side of the Earth closest to the Moon is attracted to the Moon. So is the Earth, but the Earth acts as a solid body so you can abstract it as a mass at it's center.  Since the center of the rigid Earth is farther from the Moon than the near-side water, the whole Earth moves a bit less towards the Moon than the near-side water. In other words the water level closest to the Moon rises.   The water away from the Moon is even further away than the center of the Earth, so the Earth is effective moved closer to the Moon than the water.  This gives the tidal bulges on either side.   Henry goes on with some other things including the tidal effect of a black hole (known as in the trade as spaghettification:) 

 

Jheri's question gets at something deeper.  "Why aren't there tides on ponds and lakes? Or in my coffee cup?"

 

That's a great observation  - one that never occurred to me until I was working on a homework problem in college.  There were three parts - describe the effect in simple terms, derive a formula for the tidal gravitational potential, and finally calculate the average high tide in the center of the ocean.  I answered the first part like Henry did.  The second part wasn't difficult - it was just Newtonian physics and I thought I did it properly.  Then the third part..  the numbers just didn't make sense.  I was getting sub-millimeter sized tides, but I couldn't find the flaw.  

 

Finally the answer came. The expression I derived was correct, but the my model wasn't.  Jheri is right..  If the Earth is rigid why wasn't the coffee in a cup rising?  Why wasn't I rising?  I'm not going to do the model here, but the trick is considering each point on the oceans and integrating the vector components of the forces.

 

 Imagine the Earth covered with water and the Moon orbiting over the equator.  A glob of water at the poles would be attracted to the center of the Moon.  Draw lines from the center of the Moon to these globs and you see they form an angle.  If you work out the vector components every glob of water not on the equator would have a small force pointed towards the equator.   If you add up all of these forces - do the integral - the total force is substantial.  Since water is fluid it is getting squeezed a bit.  Although each bit is small, the oceans are huge and all of those little bits add up to the tides we observe.

 

The same squeezing happens on the solid Earth, but our planet is rigid enough that the effect is small.  A tide exists in the coffee in a cup, but the total force is small enough to make them microscopic.  A large lake like Lake Michigan might build a few centimeters of tide, but you don't notice it with normal waves and wind.

 

The example in the video is sort of right - there really is differential gravity. The problem is it's about ten million times weaker than the surface gravity on Earth.  It's also an example of failure when a model is too simple and seems to be good enough.  Fortunately people like Jheri notice something's wrong which means you need a better model. 

 

claw your way to insight

Over the weekend I caught a segment on wallaby sightings in Britain.  It seems they've been zoos and private collections since the 1930s.  They're talented escape artists and many were turned out to the countryside during WWII.  Over the years there would be sightings for a year or two and then the individual would vanish.  In recent years a change has taken place and sightings are more common.  An attempt to make a census suggests there may be two breeding populations.  Momma wallabies with joeys in their pouches... 

 

In the past twenty years Britain's climate taken a major shift.   Indeed the South of England is climatically similar to wallaby-rich Tasmania.  British wallabies have few natural predators and Brits tend to love cute furry animals. It looks like they have a shot at success. 

 

Climate change.  The impact has been making marks in places we haven't thought about as well as the obvious ones we have. This one isn't too big, but it's an easy to understand example.  There are millions of others that quickly get to wicked complexity.  Mass migration, pandemics (loss of habitat is probably partly responsible for some epidemics and clearly pandemics are possible), the list of possibilities is huge.   So how do you begin to think about this class of problem?

 

The underlying physics is straightforward and known at a coarse level for about fifty years.  Thirty years ago it became clear global warming was a serious threat although it was difficult to gauge the impact.  Since then the science has become much more refined - essentially settled - and many of us became alarmed.  My conversion was about twenty years ago.  At the time I thought education would be a powerful tool and titled at those windmills for about eight years.  I didn't realize how interconnected  and nonlinear social and economic issues were. How do you communicate, how do you change minds, what is important to people?  Next regions are all different. Mix in how our brains are wired and an existential problem candidate becomes difficult to make meaningful headway on.   

 

How do you work on fundamentally difficult problems - those that are complex and non-linear?  People in my field deal with problems that tend to be much simpler, but are often too difficult to approach directly.  Early on you try to make the problem as simple as possible.  Very rough calculations often done mostly in your head or maybe a few scribbles with a stick of chalk.  The idea is to throw out a lot of bad approaches and find a few that make sense. It's playful and even exhilarating with the right people. Then you see if you can break the problem in components. It only works if the problem is decomposable with weakly interacting components.   Many problems aren't like that - the whole is much greater than the sum of the parts.   There are Nobel Prizes that have been awarded to people who have figured out clever hacks so you know how and when simple approximations can be made.  

 

Moving up to the next level of difficulty often makes careful study prone to error or even impossible.  Sometimes a way forward is possible.  A rough out of focus answer may give you the information you need to move forward. This type of integrated thinking, Murray Gell-Mann called it a coarse look at the whole or CLAW, is rare.  I've been part of three studies that used the approach.  Getting a diverse mix of people who are known to have the ability to listen to each other is important.  You need a few core experts and a mixture of generalists who recognize and build connections.  One group had a historian, psychologist, two sociologists, mathematician, two climate experts, a meteorologist, a rabbi, two computer scientists, a forestry expert, two oceanographers, a poet  and a few others including myself. (we needed a musician and chef :-) The project required two days a week face to face for two months with lots of homework. I think we had some important insights even if they were fuzzier than most of us were accustomed to.

 

There aren't many places with the structure to do this kind of coarsely focused work.  Those that do may not be as diverse as they need to be.   That said I think this can be done on a smaller scale - even with just two or three people.  Perhaps companies, government organizations and NGOs might think about tapping the power of internal diversity.  The warning is that you don't want to build internal think tanks (or even hire external ones) as that has problems of it's own. (lots of horror stories from a couple of companies I know.) 

 

A few notes from the groups I've been part of.  Counterfactuals are extremely important.  Looking at low probability, but desirable outcomes may give some insight into how to make them happen.  They can also reveal landmines you hadn't considered.   The diversity of metrics used by others can help inform your own work later on.   Picking the right people is difficult.  The success of the effort depends on it as much as anything. Understanding a bit of history can be very important. And finally a comment on simplification - the coarse graining. It needs to be discovered than imposed and that takes awhile.  A few days of conventional "brainstorming" isn't going to cut it.

 

place and time

There was a bowl of M&Ms for after the oral exams  Our grades were based on homework assignments and three oral exams. Four of us would take our turn at the blackboard. The professor had this natural ability to ask question you hadn't thought about, but should be able to solve.

 

Mr Crandall:  Does a clock at the center of the Earth run faster or slower than one on the surface?  If so how big is the difference since the Earth was formed?

(It wasn't as bad as that might sound - he was nothing like John Houseman.)

 

First a little diversion is in order.  You've probably heard the Global Positioning System needs to account for relativity.  Two effects are going on.  In one the satellites are moving with respect to GPS receiver on the ground.  Each satellite has a very stable atomic clock that is synchronized with the other GPS satellites.  Your receiver look at position and time information from at least four satellites to determine your position.  To get the necessary level of accuracy the system needs to account for the effects of both special and general relativity.   

 

Special relativity tells us moving clock appears to run a bit slower than one at rest.  Almost everything around us moves too slowly for this to be important , but a clock on a GPS satellite would lose about seven microseconds a day.  That may not seem like much, but that's enough to cause a position error that increases by about two kilometers a day. 

 

The curvature of spacetime is the bigger problem.   A result of general relativity is the direction where time runs more slowly.¹ The further a clock is from a mass, the faster it runs.  Clocks on orbiting GPS satellites gain about forty six microseconds a day.  Add the special and general relativistic effects and the satellite clocks gain a bit under thirty nine microseconds a day. Left uncorrected the system would be useless in a few minutes and the error would increase by  over seven miles in a day.   The satellites correct for both of these effects before the signal is transmitted.

 

All of this is key to the original question.  Time at the center of the Earth will pass more slowly.  The question is how much?

 

The purpose of these oral exams was not so much to test if you had learned the course material, but to encourage you to quickly frame a problem and come up with a ballpark estimate.  In the spirt of the type of education pioneered by Comenius it was  supposed to be playful and even fun.  This type of thinking with a piece of chalk is core to thinking through new ideas and working with others on certain stages of problems.  A few marks of chalk might represent dozens of pages of calculations if done in detail.  Unfortunately its protrayal on television and in movies can make the field seem artificially difficult to outsiders.

 

A quick calculation showed the center of the Earth is about 1.4 years "younger" than the surface.²  Long lived radioactive elements at the core decay slightly less than their counterparts at the surface. I can still remember the "wow" in my mind as took a handful of M&Ms. A not very great fountain of youth is under your feet. Since then I've learned exercise and eating right are better approaches to aging.

 

Since then I've done a more accurate calculation.  The inner Earth isn't homogeneous.  I found an estimate of how density changes and came up with about 2.5 years.  The initial estimate was ten or fifteen minutes with a piece of chalk vs at least a day's worth of work.   In the process I found  time dilation due to special relativity was a thousand times smaller and reasonable to ignore.  Moving to the Sun I got about 30,000 years with the simple estimate for the Sun's density.

 

The more important point is many fields develop mechanisms for dealing with either too much or too little data by coming up with simple ways to reframe and think about the task.  I've seen it in math, art and sports and assume it's a common approach to playful problem solving - probably so common you don't think about it.  The playful and fun part is key.  That's a space where you can be creative. 

 

__________

¹ You can learn special relativity with high school math and a bit of logic.  It's not at all difficult.  General relativity, on the other hand, requires much deeper math.  And a tip.  "Down is the direction where time runs more slowly" on a t-shirt is a good way to find other physicists in a crowd.

The effect is known as gravitational redshift as you usually measure this by looking at frequency shifts.  Atomic clocks are so good these days that you can measure the effect in a lab by raising one a few meters.  

2 If you want the details send me a note. First derive an equation for the gravitational potential inside a homogeneous sphere.  Next think about the frequency of a photon in a gravitation well to get change as a function of change in gravitational potential.  Then it's just remembering some constants to get the number.